As mentioned in [1]}, since the function \(\phi \)  defining the Orlicz-Sobolev spaces is usually not multiplicative, i.e., \(\phi (xy)\ne \phi (x)\phi (y)\)  for \(x,y\in \mathbb {R}\) , and the Orlicz Minkowski problem has not been completely solved, we can not use the Orlicz-Petty projection inequality [2]} and the solution of the even Orlicz Minkowski problem [3]} to prove the affine Orlicz Pólya-Szegö principle. In [1]}, making use of the functional Steiner symmetrization, the author gave a direct proof of the Orlicz Pólya-Szegö principle for log-concave functions. In this paper, we still make use of the functional Steiner symmetrization to the affine Orlicz Pólya-Szegö principle. Comparing with the paper [1]}, in this paper we mainly overcome the following several difficulties.
